The transfer function of an electrical or mechanical device may be analyzed by applying a stimulus to the device, measuring the device response and then comparing the response to the stimulus. The real and imaginary portions of the Fourier transforms of the response and stimulus signals may be determined by multiplying the signals by a complex exponential and then integrating the signals over an integral number of cycles of the frequency of interest.
Apparatus which have been constructed according to the prior art have utilized analog techniques to measure the device transfer functions. Exemplary of such prior art apparatus is the Bafco Co., Inc., Model No. 916 Universal Two Channel Sweep Frequency Response Analyzer which applies an analog stimulus signal to a device and then integrates the analog stimulus and response signals as part of the measurement of the transfer function. Such prior art apparatus require the use of analog computational methods which tend to be less accurate than comparable digital methods.
In accordance with the illustrated preferred embodiment of the present invention, a transfer function analyzer accurately and efficiently performs transfer function analyses using digital techniques. The analyzer applies a stimulus signal to a device, samples the stimulus signal and the resulting response signal, multiplies both signals by a discrete complex exponential and integrates the multiplied signals to yield the Fourier transforms of the stimulus and response signals. The transfer function may then be found by dividing the Fourier transform of the response signal by the Fourier transform of the stimulus signal. Measurement of the integral of each multiplied signal is performed by summing a central sector of data points and by adding to this sum both a preceding sector multiplied by a data independent preceding weighting function and a succeeding sector multiplied by a data independent succeeding weighting function.
The analyzer is capable of determining the transfer function of a device at any stimulus signal frequency within a given range. Accuracy is independent of the period of the stimulus signal and of the relationship between the stimulus signal frequency and the sample rate. Thus, it is not necessary for the period of integration to begin or end at a discrete data point. If, for example, the period ends between two adjacent discrete data points, then the analyzer uses a modified succeeding weighting polynomial to measure the integral between the two adjacent discrete data points. Thus, measurement accuracy does not change with changes in the frequency of the stimulus signal.